Objective-Sensitive Principal Component Analysis for High-Dimensional Inverse Problems

• URL: http://arxiv.org/abs/2006.04527v1
• Date: Tue, 2 Jun 2020 18:51:17 GMT
• Title: Objective-Sensitive Principal Component Analysis for High-Dimensional Inverse Problems
• Authors: Maksim Elizarev, Andrei Mukhin and Aleksey Khlyupin
• Abstract summary: We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. The developed technique is based on principal component analysis (PCA) but modifies a purely data-driven basis of principal components considering objective function behavior. Three algorithms for optimal parameter decomposition are presented and applied to an objective of 2D synthetic history matching.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems, including history matching. The developed technique is based on principal component analysis (PCA) but modifies a purely data-driven basis of principal components considering objective function behavior. To define an efficient encoding, Gradient-Sensitive PCA uses an objective function gradient with respect to model parameters. We propose computationally efficient implementations of the technique, and two of them are based on stationary perturbation theory (SPT). Optimality, correctness, and low computational costs of the new encoding approach are tested, verified, and discussed. Three algorithms for optimal parameter decomposition are presented and applied to an objective of 2D synthetic history matching. The results demonstrate improvements in encoding quality regarding objective function minimization and distributional patterns of the desired field. Possible applications and extensions are proposed.

Related papers

• Multi-objective Memetic Algorithm with Adaptive Weights for Inverse Antenna Design [0.0]
  modification of a single-objective algorithm into its multi-objective counterpart. Result is a considerable increase in speed in the order of tens to hundreds.
  arXiv  Detail & Related papers  (2024-08-07T08:43:38Z)
• Simultaneous and Meshfree Topology Optimization with Physics-informed Gaussian Processes [0.0]
  Topology optimization (TO) provides a principled mathematical approach for optimizing the performance of a structure by designing its material spatial distribution in a pre-defined domain and subject to a set of constraints. We develop a new class of TO methods based on the framework of Gaussian processes (GPs) whose mean functions are parameterized via deep neural networks. To test our method against conventional TO approaches implemented in commercial software, we evaluate it on four problems involving the minimization of dissipated power in Stokes flow.
  arXiv  Detail & Related papers  (2024-08-07T01:01:35Z)
• End-to-End Learning for Fair Multiobjective Optimization Under Uncertainty [55.04219793298687]
  The Predict-Then-Forecast (PtO) paradigm in machine learning aims to maximize downstream decision quality. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives. It shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.
  arXiv  Detail & Related papers  (2024-02-12T16:33:35Z)
• Implicit Rate-Constrained Optimization of Non-decomposable Objectives [37.43791617018009]
  We consider a family of constrained optimization problems arising in machine learning. Our key idea is to formulate a rate-constrained optimization that expresses the threshold parameter as a function of the model parameters. We show how the resulting optimization problem can be solved using standard gradient based methods.
  arXiv  Detail & Related papers  (2021-07-23T00:04:39Z)
• Robust Topology Optimization Using Multi-Fidelity Variational Autoencoders [1.0124625066746595]
  A robust topology optimization (RTO) problem identifies a design with the best average performance. A neural network method is proposed that offers computational efficiency. Numerical application of the method is shown on the robust design of L-bracket structure with single point load as well as multiple point loads.
  arXiv  Detail & Related papers  (2021-07-19T20:40:51Z)
• Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box Optimization Framework [100.36569795440889]
  This work is on the iteration of zero-th-order (ZO) optimization which does not require first-order information. We show that with a graceful design in coordinate importance sampling, the proposed ZO optimization method is efficient both in terms of complexity as well as as function query cost.
  arXiv  Detail & Related papers  (2020-12-21T17:29:58Z)
• An AI-Assisted Design Method for Topology Optimization Without Pre-Optimized Training Data [68.8204255655161]
  An AI-assisted design method based on topology optimization is presented, which is able to obtain optimized designs in a direct way. Designs are provided by an artificial neural network, the predictor, on the basis of boundary conditions and degree of filling as input data.
  arXiv  Detail & Related papers  (2020-12-11T14:33:27Z)
• Logistic Q-Learning [87.00813469969167]
  We propose a new reinforcement learning algorithm derived from a regularized linear-programming formulation of optimal control in MDPs. The main feature of our algorithm is a convex loss function for policy evaluation that serves as a theoretically sound alternative to the widely used squared Bellman error.
  arXiv  Detail & Related papers  (2020-10-21T17:14:31Z)
• Bilevel Optimization: Convergence Analysis and Enhanced Design [63.64636047748605]
  Bilevel optimization is a tool for many machine learning problems. We propose a novel stoc-efficientgradient estimator named stoc-BiO.
  arXiv  Detail & Related papers  (2020-10-15T18:09:48Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• On the implementation of a global optimization method for mixed-variable problems [0.30458514384586394]
  The algorithm is based on the radial basis function of Gutmann and the metric response surface method of Regis and Shoemaker. We propose several modifications aimed at generalizing and improving these two algorithms.
  arXiv  Detail & Related papers  (2020-09-04T13:36:56Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.